Some of this isn't making sense.
iTunes accounts cannot be split. While you can put a copy, or even move a file, of media purchased in your own library on a computer, the media itself will remain permanently attached to the iTunes online account with which it is purchased.
The only way I can think of that you are seeing what you say is if you added a file from your mother's library to your library on the computer, then delete it from your library on the computer (not your account which is something in Apple's Cloud) and in doing so it removes the file to which your mother's library is pointing...
I guess the other possibility is your mother didn't have an account in the first place and although you were using her iTunes library on the computer it was really using your iTunes account...